{
  "abstract": "The fate of average symmetry-protected topological (ASPT) states based on the one-dimensional cluster state is investigated by using the Choi mapping, namely, the doubled Hilbert-space formalism. By introducing two effective spins, $τ$ and $η$, on each doubled rung, we obtain a transparent representation of the ASPT parent Hamiltonian and systematically identify the conserved stabilizers and the corresponding orders. We further study symmetry-preserving operations that deform the ASPT by combining qualitative effective-Hamiltonian and systematic parent-Hamiltonian analyses with numerical matrix-product-state filtering calculations. We find that although the ASPT remains robust over a broad range of decoherence strengths, strong-to-weak spontaneous symmetry breaking (SWSSB) becomes exact in the maximal-decoherence limit. In addition, we consider symmetry preserving no-click postselection, which removes the exact conservation law supporting the Rényi-2 string order of the ASPT and drives the system toward weak-symmetry spontaneous symmetry breaking (WSSB). Again, the ASPT remains robust over a broad range of postselection strengths, with WSSB becoming pronounced only near the projective limit and exact at the limit itself.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27530",
  "author_total": 2,
  "authors": [
    {
      "name": "Yoshihito Kuno"
    },
    {
      "name": "Takahiro Orito"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1bh55d2yd205r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27530",
  "fulltext_url": null,
  "id": "1bh55d2yd205r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27530",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7214226023",
  "pdf_url": "https://arxiv.org/pdf/2609.27530",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1bh55d2yd205r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.27530",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27530"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Fate of average symmetry-protected topological states under symmetry-preserving quantum operations",
  "title_text": "Fate of average symmetry-protected topological states under symmetry-preserving quantum operations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:56Z",
  "url": "https://research.draconitic.com/paper/1bh55d2yd205r",
  "venue": "arXiv",
  "versions": []
}